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% Special Issue
% "Evolutionary Multiobjective Optimization: Methodologies and Applications"
% of the Journal of Multi-Criteria Decision Analysis (Wiley)
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% guest editors: Dimo Brockhoff and Kalyanmoy Deb
\documentclass{article}
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\newcommand{\DTLZBZ}{\ensuremath{\text{DTLZ}_{\text{BZ}}}\xspace}


\title{New Many-Objective Test Problems for Benchmarking Objective Reduction Algorithms}

\author{Dimo Brockhoff\\
System Modeling and Optimization Team (sysmo)\\
Laboratoire d'Informatique (LIX)\\
\'{E}cole Polytechnique\\
91128 Palaiseau Cedex, France\\
\url{brockho@lix.polytechnique.fr}\\
\and
Kalyanmoy Deb\\
Indian Institute of Technology Kanpur\\
Kanpur, India
\url{deb@iitk.ac.in}\\
\and
Anmol Pandey\\
Indian Institute of Technology Kanpur\\
Kanpur, India
}
\date{}



\begin{document}

\maketitle

\begin{abstract}
		Many scalable benchmark problems are known in the field of Evolutionary Multiobjective Optimization (EMO) and several of them have been used in the scope of many-objective optimization when the number of objectives is larger than 3. In particular when assessing automated objective reduction algorithms, the well-known test functions such as the ones from the DTLZ or WFG test function suites, some drawbacks of these problems can be observed. The main concern is that the conflict between the objectives (or their correlation) is not or only slightly changing during the search with EMO methods. Here, we therefore propose new versions of the standard test functions that exhibit varying conflict among the objectives.
\end{abstract}


\section{Introduction}

\section{Conflicts and Correlations Among Objectives}

\section{The Standard DTLZ and WFG Problems}

\section{Known Variations of DTLZ Problems}
\begin{itemize}
	\item many-objective DTLZ5(M,I) problems with front lower-dimensional (dimension I) than entire objective space (M objectives)
	\item \DTLZBZ problems: (i) omission of $<M-1$ objectives does not always result in 1 Pareto-optimal point only and (ii) omitted objectives are not automatically optimized due to high correlation (distance to front does not appear in all objectives as the same factor anymore)
\end{itemize}

\section{Introducing Varying Conflicts in the DTLZ Problems}

\section{Experimentation}



\end{document}
